I was at the Mayo Clinic many years ago and a requirement to get into the pain clinic was an EMG. Knowing that I was highly sensitive to even "touch" I knew that would really do me in. Thus I refused. Later saw a neurologist there who said I did the correct thing considering my high level of sensitivity. Then just a few years ago another to specialist insisted on an EMG> Once again I refused and I haven't seen him since.
I have a hyperactive nervous system and know those needles would trigger off more pain.
I am so sorry that you are experiencing difficult with your arm. I do hope it subsides. Perhaps you could call and ask for their advice on what to do about it. By the way - why did they want to do this to you if they even suspected RSD.
Best wishes
Sydney